On the Complexity of Parallel Coordinate Descent

In this work we study the parallel coordinate descent method (PCDM) proposed by Richtárik and Takáč [26] for minimizing a regularized convex function. We adopt elements from the work of Xiao and Lu [39], and combine them with several new insights, to obtain sharper iteration complexity results for P...

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Veröffentlicht in:arXiv.org 2015-03
Hauptverfasser: Tappenden, Rachael, Takáč, Martin, Richtárik, Peter
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Sprache:eng
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Zusammenfassung:In this work we study the parallel coordinate descent method (PCDM) proposed by Richtárik and Takáč [26] for minimizing a regularized convex function. We adopt elements from the work of Xiao and Lu [39], and combine them with several new insights, to obtain sharper iteration complexity results for PCDM than those presented in [26]. Moreover, we show that PCDM is monotonic in expectation, which was not confirmed in [26], and we also derive the first high probability iteration complexity result where the initial levelset is unbounded.
ISSN:2331-8422